// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_CXX11_TENSOR_TENSOR_INDEX_LIST_H
#define EIGEN_CXX11_TENSOR_TENSOR_INDEX_LIST_H

#if EIGEN_HAS_CONSTEXPR && EIGEN_HAS_VARIADIC_TEMPLATES

#define EIGEN_HAS_INDEX_LIST

namespace Eigen {

/** \internal
  *
  * \class TensorIndexList
  * \ingroup CXX11_Tensor_Module
  *
  * \brief Set of classes used to encode a set of Tensor dimensions/indices.
  *
  * The indices in the list can be known at compile time or at runtime. A mix
  * of static and dynamic indices can also be provided if needed. The tensor
  * code will attempt to take advantage of the indices that are known at
  * compile time to optimize the code it generates.
  *
  * This functionality requires a c++11 compliant compiler. If your compiler
  * is older you need to use arrays of indices instead.
  *
  * Several examples are provided in the cxx11_tensor_index_list.cpp file.
  *
  * \sa Tensor
  */

template <Index n> struct type2index
{
    static const Index value = n;
    EIGEN_DEVICE_FUNC constexpr operator Index() const { return n; }
    EIGEN_DEVICE_FUNC void set(Index val) { eigen_assert(val == n); }
};

// This can be used with IndexPairList to get compile-time constant pairs,
// such as IndexPairList<type2indexpair<1,2>, type2indexpair<3,4>>().
template <Index f, Index s> struct type2indexpair
{
    static const Index first = f;
    static const Index second = s;

    constexpr EIGEN_DEVICE_FUNC operator IndexPair<Index>() const { return IndexPair<Index>(f, s); }

    EIGEN_DEVICE_FUNC void set(const IndexPair<Index>& val)
    {
        eigen_assert(val.first == f);
        eigen_assert(val.second == s);
    }
};

template <Index n> struct NumTraits<type2index<n>>
{
    typedef Index Real;
    enum
    {
        IsComplex = 0,
        RequireInitialization = false,
        ReadCost = 1,
        AddCost = 1,
        MulCost = 1
    };

    EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR EIGEN_STRONG_INLINE Real epsilon() { return 0; }
    EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR EIGEN_STRONG_INLINE Real dummy_precision() { return 0; }
    EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR EIGEN_STRONG_INLINE Real highest() { return n; }
    EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR EIGEN_STRONG_INLINE Real lowest() { return n; }
};

namespace internal {
    template <typename T> EIGEN_DEVICE_FUNC void update_value(T& val, Index new_val) { val = internal::convert_index<T>(new_val); }
    template <Index n> EIGEN_DEVICE_FUNC void update_value(type2index<n>& val, Index new_val) { val.set(new_val); }

    template <typename T> EIGEN_DEVICE_FUNC void update_value(T& val, IndexPair<Index> new_val) { val = new_val; }
    template <Index f, Index s> EIGEN_DEVICE_FUNC void update_value(type2indexpair<f, s>& val, IndexPair<Index> new_val) { val.set(new_val); }

    template <typename T> struct is_compile_time_constant
    {
        static constexpr bool value = false;
    };

    template <Index idx> struct is_compile_time_constant<type2index<idx>>
    {
        static constexpr bool value = true;
    };
    template <Index idx> struct is_compile_time_constant<const type2index<idx>>
    {
        static constexpr bool value = true;
    };
    template <Index idx> struct is_compile_time_constant<type2index<idx>&>
    {
        static constexpr bool value = true;
    };
    template <Index idx> struct is_compile_time_constant<const type2index<idx>&>
    {
        static constexpr bool value = true;
    };

    template <Index f, Index s> struct is_compile_time_constant<type2indexpair<f, s>>
    {
        static constexpr bool value = true;
    };
    template <Index f, Index s> struct is_compile_time_constant<const type2indexpair<f, s>>
    {
        static constexpr bool value = true;
    };
    template <Index f, Index s> struct is_compile_time_constant<type2indexpair<f, s>&>
    {
        static constexpr bool value = true;
    };
    template <Index f, Index s> struct is_compile_time_constant<const type2indexpair<f, s>&>
    {
        static constexpr bool value = true;
    };

    template <typename... T> struct IndexTuple;

    template <typename T, typename... O> struct IndexTuple<T, O...>
    {
        EIGEN_DEVICE_FUNC constexpr IndexTuple() : head(), others() {}
        EIGEN_DEVICE_FUNC constexpr IndexTuple(const T& v, const O... o) : head(v), others(o...) {}

        constexpr static int count = 1 + sizeof...(O);
        T head;
        IndexTuple<O...> others;
        typedef T Head;
        typedef IndexTuple<O...> Other;
    };

    template <typename T> struct IndexTuple<T>
    {
        EIGEN_DEVICE_FUNC constexpr IndexTuple() : head() {}
        EIGEN_DEVICE_FUNC constexpr IndexTuple(const T& v) : head(v) {}

        constexpr static int count = 1;
        T head;
        typedef T Head;
    };

    template <int N, typename... T> struct IndexTupleExtractor;

    template <int N, typename T, typename... O> struct IndexTupleExtractor<N, T, O...>
    {
        typedef typename IndexTupleExtractor<N - 1, O...>::ValType ValType;

        EIGEN_DEVICE_FUNC static constexpr ValType& get_val(IndexTuple<T, O...>& val) { return IndexTupleExtractor<N - 1, O...>::get_val(val.others); }

        EIGEN_DEVICE_FUNC static constexpr const ValType& get_val(const IndexTuple<T, O...>& val)
        {
            return IndexTupleExtractor<N - 1, O...>::get_val(val.others);
        }
        template <typename V> EIGEN_DEVICE_FUNC static void set_val(IndexTuple<T, O...>& val, V& new_val)
        {
            IndexTupleExtractor<N - 1, O...>::set_val(val.others, new_val);
        }
    };

    template <typename T, typename... O> struct IndexTupleExtractor<0, T, O...>
    {
        typedef T ValType;

        EIGEN_DEVICE_FUNC static constexpr ValType& get_val(IndexTuple<T, O...>& val) { return val.head; }
        EIGEN_DEVICE_FUNC static constexpr const ValType& get_val(const IndexTuple<T, O...>& val) { return val.head; }
        template <typename V> EIGEN_DEVICE_FUNC static void set_val(IndexTuple<T, O...>& val, V& new_val) { val.head = new_val; }
    };

    template <int N, typename T, typename... O>
    EIGEN_DEVICE_FUNC constexpr typename IndexTupleExtractor<N, T, O...>::ValType& array_get(IndexTuple<T, O...>& tuple)
    {
        return IndexTupleExtractor<N, T, O...>::get_val(tuple);
    }
    template <int N, typename T, typename... O>
    EIGEN_DEVICE_FUNC constexpr const typename IndexTupleExtractor<N, T, O...>::ValType& array_get(const IndexTuple<T, O...>& tuple)
    {
        return IndexTupleExtractor<N, T, O...>::get_val(tuple);
    }
    template <typename T, typename... O> struct array_size<IndexTuple<T, O...>>
    {
        static const size_t value = IndexTuple<T, O...>::count;
    };
    template <typename T, typename... O> struct array_size<const IndexTuple<T, O...>>
    {
        static const size_t value = IndexTuple<T, O...>::count;
    };

    template <Index Idx, typename ValueT> struct tuple_coeff
    {
        template <typename... T> EIGEN_DEVICE_FUNC static constexpr ValueT get(const Index i, const IndexTuple<T...>& t)
        {
            //    return array_get<Idx>(t) * (i == Idx) + tuple_coeff<Idx-1>::get(i, t) * (i != Idx);
            return (i == Idx ? array_get<Idx>(t) : tuple_coeff<Idx - 1, ValueT>::get(i, t));
        }
        template <typename... T> EIGEN_DEVICE_FUNC static void set(const Index i, IndexTuple<T...>& t, const ValueT& value)
        {
            if (i == Idx)
            {
                update_value(array_get<Idx>(t), value);
            }
            else
            {
                tuple_coeff<Idx - 1, ValueT>::set(i, t, value);
            }
        }

        template <typename... T> EIGEN_DEVICE_FUNC static constexpr bool value_known_statically(const Index i, const IndexTuple<T...>& t)
        {
            return ((i == Idx) & is_compile_time_constant<typename IndexTupleExtractor<Idx, T...>::ValType>::value) ||
                   tuple_coeff<Idx - 1, ValueT>::value_known_statically(i, t);
        }

        template <typename... T> EIGEN_DEVICE_FUNC static constexpr bool values_up_to_known_statically(const IndexTuple<T...>& t)
        {
            return is_compile_time_constant<typename IndexTupleExtractor<Idx, T...>::ValType>::value &&
                   tuple_coeff<Idx - 1, ValueT>::values_up_to_known_statically(t);
        }

        template <typename... T> EIGEN_DEVICE_FUNC static constexpr bool values_up_to_statically_known_to_increase(const IndexTuple<T...>& t)
        {
            return is_compile_time_constant<typename IndexTupleExtractor<Idx, T...>::ValType>::value &&
                   is_compile_time_constant<typename IndexTupleExtractor<Idx, T...>::ValType>::value && array_get<Idx>(t) > array_get<Idx - 1>(t) &&
                   tuple_coeff<Idx - 1, ValueT>::values_up_to_statically_known_to_increase(t);
        }
    };

    template <typename ValueT> struct tuple_coeff<0, ValueT>
    {
        template <typename... T> EIGEN_DEVICE_FUNC static constexpr ValueT get(const Index /*i*/, const IndexTuple<T...>& t)
        {
            //  eigen_assert (i == 0);  // gcc fails to compile assertions in constexpr
            return array_get<0>(t) /* * (i == 0)*/;
        }
        template <typename... T> EIGEN_DEVICE_FUNC static void set(const Index i, IndexTuple<T...>& t, const ValueT value)
        {
            eigen_assert(i == 0);
            update_value(array_get<0>(t), value);
        }
        template <typename... T> EIGEN_DEVICE_FUNC static constexpr bool value_known_statically(const Index i, const IndexTuple<T...>&)
        {
            return is_compile_time_constant<typename IndexTupleExtractor<0, T...>::ValType>::value && (i == 0);
        }

        template <typename... T> EIGEN_DEVICE_FUNC static constexpr bool values_up_to_known_statically(const IndexTuple<T...>&)
        {
            return is_compile_time_constant<typename IndexTupleExtractor<0, T...>::ValType>::value;
        }

        template <typename... T> EIGEN_DEVICE_FUNC static constexpr bool values_up_to_statically_known_to_increase(const IndexTuple<T...>&) { return true; }
    };
}  // namespace internal

template <typename FirstType, typename... OtherTypes> struct IndexList : internal::IndexTuple<FirstType, OtherTypes...>
{
    EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC constexpr Index operator[](const Index i) const
    {
        return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...>>::value - 1, Index>::get(i, *this);
    }
    EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC constexpr Index get(const Index i) const
    {
        return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...>>::value - 1, Index>::get(i, *this);
    }
    EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC void set(const Index i, const Index value)
    {
        return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...>>::value - 1, Index>::set(i, *this, value);
    }

    EIGEN_DEVICE_FUNC constexpr IndexList(const internal::IndexTuple<FirstType, OtherTypes...>& other) : internal::IndexTuple<FirstType, OtherTypes...>(other)
    {
    }
    EIGEN_DEVICE_FUNC constexpr IndexList(FirstType& first, OtherTypes... other) : internal::IndexTuple<FirstType, OtherTypes...>(first, other...) {}
    EIGEN_DEVICE_FUNC constexpr IndexList() : internal::IndexTuple<FirstType, OtherTypes...>() {}

    EIGEN_DEVICE_FUNC constexpr bool value_known_statically(const Index i) const
    {
        return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...>>::value - 1, Index>::value_known_statically(i, *this);
    }
    EIGEN_DEVICE_FUNC constexpr bool all_values_known_statically() const
    {
        return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...>>::value - 1, Index>::values_up_to_known_statically(
            *this);
    }

    EIGEN_DEVICE_FUNC constexpr bool values_statically_known_to_increase() const
    {
        return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...>>::value - 1,
                                     Index>::values_up_to_statically_known_to_increase(*this);
    }
};

template <typename FirstType, typename... OtherTypes> std::ostream& operator<<(std::ostream& os, const IndexList<FirstType, OtherTypes...>& dims)
{
    os << "[";
    for (size_t i = 0; i < 1 + sizeof...(OtherTypes); ++i)
    {
        if (i > 0)
            os << ", ";
        os << dims[i];
    }
    os << "]";
    return os;
}

template <typename FirstType, typename... OtherTypes> constexpr IndexList<FirstType, OtherTypes...> make_index_list(FirstType val1, OtherTypes... other_vals)
{
    return IndexList<FirstType, OtherTypes...>(val1, other_vals...);
}

template <typename FirstType, typename... OtherTypes> struct IndexPairList : internal::IndexTuple<FirstType, OtherTypes...>
{
    EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC constexpr IndexPair<Index> operator[](const Index i) const
    {
        return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...>>::value - 1, IndexPair<Index>>::get(i, *this);
    }
    EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC void set(const Index i, const IndexPair<Index> value)
    {
        return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...>>::value - 1, IndexPair<Index>>::set(i, *this, value);
    }

    EIGEN_DEVICE_FUNC constexpr IndexPairList(const internal::IndexTuple<FirstType, OtherTypes...>& other)
        : internal::IndexTuple<FirstType, OtherTypes...>(other)
    {
    }
    EIGEN_DEVICE_FUNC constexpr IndexPairList() : internal::IndexTuple<FirstType, OtherTypes...>() {}

    EIGEN_DEVICE_FUNC constexpr bool value_known_statically(const Index i) const
    {
        return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...>>::value - 1, Index>::value_known_statically(i, *this);
    }
};

namespace internal {

    template <typename FirstType, typename... OtherTypes>
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index array_prod(const IndexList<FirstType, OtherTypes...>& sizes)
    {
        Index result = 1;
        EIGEN_UNROLL_LOOP
        for (size_t i = 0; i < array_size<IndexList<FirstType, OtherTypes...>>::value; ++i) { result *= sizes[i]; }
        return result;
    }

    template <typename FirstType, typename... OtherTypes> struct array_size<IndexList<FirstType, OtherTypes...>>
    {
        static const size_t value = array_size<IndexTuple<FirstType, OtherTypes...>>::value;
    };
    template <typename FirstType, typename... OtherTypes> struct array_size<const IndexList<FirstType, OtherTypes...>>
    {
        static const size_t value = array_size<IndexTuple<FirstType, OtherTypes...>>::value;
    };

    template <typename FirstType, typename... OtherTypes> struct array_size<IndexPairList<FirstType, OtherTypes...>>
    {
        static const size_t value = std::tuple_size<std::tuple<FirstType, OtherTypes...>>::value;
    };
    template <typename FirstType, typename... OtherTypes> struct array_size<const IndexPairList<FirstType, OtherTypes...>>
    {
        static const size_t value = std::tuple_size<std::tuple<FirstType, OtherTypes...>>::value;
    };

    template <Index N, typename FirstType, typename... OtherTypes> EIGEN_DEVICE_FUNC constexpr Index array_get(IndexList<FirstType, OtherTypes...>& a)
    {
        return IndexTupleExtractor<N, FirstType, OtherTypes...>::get_val(a);
    }
    template <Index N, typename FirstType, typename... OtherTypes> EIGEN_DEVICE_FUNC constexpr Index array_get(const IndexList<FirstType, OtherTypes...>& a)
    {
        return IndexTupleExtractor<N, FirstType, OtherTypes...>::get_val(a);
    }

    template <typename T> struct index_known_statically_impl
    {
        EIGEN_DEVICE_FUNC static constexpr bool run(const Index) { return false; }
    };

    template <typename FirstType, typename... OtherTypes> struct index_known_statically_impl<IndexList<FirstType, OtherTypes...>>
    {
        EIGEN_DEVICE_FUNC static constexpr bool run(const Index i) { return IndexList<FirstType, OtherTypes...>().value_known_statically(i); }
    };

    template <typename FirstType, typename... OtherTypes> struct index_known_statically_impl<const IndexList<FirstType, OtherTypes...>>
    {
        EIGEN_DEVICE_FUNC static constexpr bool run(const Index i) { return IndexList<FirstType, OtherTypes...>().value_known_statically(i); }
    };

    template <typename T> struct all_indices_known_statically_impl
    {
        static constexpr bool run() { return false; }
    };

    template <typename FirstType, typename... OtherTypes> struct all_indices_known_statically_impl<IndexList<FirstType, OtherTypes...>>
    {
        EIGEN_DEVICE_FUNC static constexpr bool run() { return IndexList<FirstType, OtherTypes...>().all_values_known_statically(); }
    };

    template <typename FirstType, typename... OtherTypes> struct all_indices_known_statically_impl<const IndexList<FirstType, OtherTypes...>>
    {
        EIGEN_DEVICE_FUNC static constexpr bool run() { return IndexList<FirstType, OtherTypes...>().all_values_known_statically(); }
    };

    template <typename T> struct indices_statically_known_to_increase_impl
    {
        EIGEN_DEVICE_FUNC static constexpr bool run() { return false; }
    };

    template <typename FirstType, typename... OtherTypes> struct indices_statically_known_to_increase_impl<IndexList<FirstType, OtherTypes...>>
    {
        EIGEN_DEVICE_FUNC static constexpr bool run() { return Eigen::IndexList<FirstType, OtherTypes...>().values_statically_known_to_increase(); }
    };

    template <typename FirstType, typename... OtherTypes> struct indices_statically_known_to_increase_impl<const IndexList<FirstType, OtherTypes...>>
    {
        EIGEN_DEVICE_FUNC static constexpr bool run() { return Eigen::IndexList<FirstType, OtherTypes...>().values_statically_known_to_increase(); }
    };

    template <typename Tx> struct index_statically_eq_impl
    {
        EIGEN_DEVICE_FUNC static constexpr bool run(Index, Index) { return false; }
    };

    template <typename FirstType, typename... OtherTypes> struct index_statically_eq_impl<IndexList<FirstType, OtherTypes...>>
    {
        EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value)
        {
            return IndexList<FirstType, OtherTypes...>().value_known_statically(i) & (IndexList<FirstType, OtherTypes...>().get(i) == value);
        }
    };

    template <typename FirstType, typename... OtherTypes> struct index_statically_eq_impl<const IndexList<FirstType, OtherTypes...>>
    {
        EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value)
        {
            return IndexList<FirstType, OtherTypes...>().value_known_statically(i) & (IndexList<FirstType, OtherTypes...>().get(i) == value);
        }
    };

    template <typename T> struct index_statically_ne_impl
    {
        EIGEN_DEVICE_FUNC static constexpr bool run(Index, Index) { return false; }
    };

    template <typename FirstType, typename... OtherTypes> struct index_statically_ne_impl<IndexList<FirstType, OtherTypes...>>
    {
        EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value)
        {
            return IndexList<FirstType, OtherTypes...>().value_known_statically(i) & (IndexList<FirstType, OtherTypes...>().get(i) != value);
        }
    };

    template <typename FirstType, typename... OtherTypes> struct index_statically_ne_impl<const IndexList<FirstType, OtherTypes...>>
    {
        EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value)
        {
            return IndexList<FirstType, OtherTypes...>().value_known_statically(i) & (IndexList<FirstType, OtherTypes...>().get(i) != value);
        }
    };

    template <typename T> struct index_statically_gt_impl
    {
        EIGEN_DEVICE_FUNC static constexpr bool run(Index, Index) { return false; }
    };

    template <typename FirstType, typename... OtherTypes> struct index_statically_gt_impl<IndexList<FirstType, OtherTypes...>>
    {
        EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value)
        {
            return IndexList<FirstType, OtherTypes...>().value_known_statically(i) & (IndexList<FirstType, OtherTypes...>().get(i) > value);
        }
    };

    template <typename FirstType, typename... OtherTypes> struct index_statically_gt_impl<const IndexList<FirstType, OtherTypes...>>
    {
        EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value)
        {
            return IndexList<FirstType, OtherTypes...>().value_known_statically(i) & (IndexList<FirstType, OtherTypes...>().get(i) > value);
        }
    };

    template <typename T> struct index_statically_lt_impl
    {
        EIGEN_DEVICE_FUNC static constexpr bool run(Index, Index) { return false; }
    };

    template <typename FirstType, typename... OtherTypes> struct index_statically_lt_impl<IndexList<FirstType, OtherTypes...>>
    {
        EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value)
        {
            return IndexList<FirstType, OtherTypes...>().value_known_statically(i) & (IndexList<FirstType, OtherTypes...>().get(i) < value);
        }
    };

    template <typename FirstType, typename... OtherTypes> struct index_statically_lt_impl<const IndexList<FirstType, OtherTypes...>>
    {
        EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value)
        {
            return IndexList<FirstType, OtherTypes...>().value_known_statically(i) & (IndexList<FirstType, OtherTypes...>().get(i) < value);
        }
    };

    template <typename Tx> struct index_pair_first_statically_eq_impl
    {
        EIGEN_DEVICE_FUNC static constexpr bool run(Index, Index) { return false; }
    };

    template <typename FirstType, typename... OtherTypes> struct index_pair_first_statically_eq_impl<IndexPairList<FirstType, OtherTypes...>>
    {
        EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value)
        {
            return IndexPairList<FirstType, OtherTypes...>().value_known_statically(i) &
                   (IndexPairList<FirstType, OtherTypes...>().operator[](i).first == value);
        }
    };

    template <typename FirstType, typename... OtherTypes> struct index_pair_first_statically_eq_impl<const IndexPairList<FirstType, OtherTypes...>>
    {
        EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value)
        {
            return IndexPairList<FirstType, OtherTypes...>().value_known_statically(i) &
                   (IndexPairList<FirstType, OtherTypes...>().operator[](i).first == value);
        }
    };

    template <typename Tx> struct index_pair_second_statically_eq_impl
    {
        EIGEN_DEVICE_FUNC static constexpr bool run(Index, Index) { return false; }
    };

    template <typename FirstType, typename... OtherTypes> struct index_pair_second_statically_eq_impl<IndexPairList<FirstType, OtherTypes...>>
    {
        EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value)
        {
            return IndexPairList<FirstType, OtherTypes...>().value_known_statically(i) &
                   (IndexPairList<FirstType, OtherTypes...>().operator[](i).second == value);
        }
    };

    template <typename FirstType, typename... OtherTypes> struct index_pair_second_statically_eq_impl<const IndexPairList<FirstType, OtherTypes...>>
    {
        EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value)
        {
            return IndexPairList<FirstType, OtherTypes...>().value_known_statically(i) &
                   (IndexPairList<FirstType, OtherTypes...>().operator[](i).second == value);
        }
    };

}  // end namespace internal
}  // end namespace Eigen

#else

namespace Eigen {
namespace internal {

    template <typename T> struct index_known_statically_impl
    {
        static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run(const Index) { return false; }
    };

    template <typename T> struct all_indices_known_statically_impl
    {
        static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run() { return false; }
    };

    template <typename T> struct indices_statically_known_to_increase_impl
    {
        static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run() { return false; }
    };

    template <typename T> struct index_statically_eq_impl
    {
        static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run(Index, Index) { return false; }
    };

    template <typename T> struct index_statically_ne_impl
    {
        static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run(Index, Index) { return false; }
    };

    template <typename T> struct index_statically_gt_impl
    {
        static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run(Index, Index) { return false; }
    };

    template <typename T> struct index_statically_lt_impl
    {
        static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run(Index, Index) { return false; }
    };

    template <typename Tx> struct index_pair_first_statically_eq_impl
    {
        static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run(Index, Index) { return false; }
    };

    template <typename Tx> struct index_pair_second_statically_eq_impl
    {
        static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run(Index, Index) { return false; }
    };

}  // end namespace internal
}  // end namespace Eigen

#endif

namespace Eigen {
namespace internal {
    template <typename T> static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool index_known_statically(Index i) { return index_known_statically_impl<T>::run(i); }

    template <typename T> static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool all_indices_known_statically() { return all_indices_known_statically_impl<T>::run(); }

    template <typename T> static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool indices_statically_known_to_increase()
    {
        return indices_statically_known_to_increase_impl<T>::run();
    }

    template <typename T> static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool index_statically_eq(Index i, Index value)
    {
        return index_statically_eq_impl<T>::run(i, value);
    }

    template <typename T> static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool index_statically_ne(Index i, Index value)
    {
        return index_statically_ne_impl<T>::run(i, value);
    }

    template <typename T> static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool index_statically_gt(Index i, Index value)
    {
        return index_statically_gt_impl<T>::run(i, value);
    }

    template <typename T> static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool index_statically_lt(Index i, Index value)
    {
        return index_statically_lt_impl<T>::run(i, value);
    }

    template <typename T> static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool index_pair_first_statically_eq(Index i, Index value)
    {
        return index_pair_first_statically_eq_impl<T>::run(i, value);
    }

    template <typename T> static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool index_pair_second_statically_eq(Index i, Index value)
    {
        return index_pair_second_statically_eq_impl<T>::run(i, value);
    }

}  // end namespace internal
}  // end namespace Eigen

#endif  // EIGEN_CXX11_TENSOR_TENSOR_INDEX_LIST_H
